Differential Equations and Dynamical Systems Group

The main areas of research of the Differential Equations and Dynamical Systems Group:
1. Applications of measure theory, topological and computer assisted methods in the investigation of discrete and continuous dynamical systems. In particular: the phenomena of chaos in discrete dynamical systems, investigation of normally hyperbolic invariant manifolds in continuous dynamical systems, Conley index theory.
2. Investigation of nonlinear functional differential equations of parabolic and elliptic type. In particular: existence and uniqueness of solutions of infinite systems of equations of the above types; convergence and stability of the difference methods for such systems.
3. Applications of the methods based on Lie group theory, qualitative and functional methods of construction of the solutions of nonlinear equations of mathematical biology and physics and the investigation of their properties (in particular solutions of concentrated wave patterns and their interactions). Moreover investigation of the convection-reaction-diffusion equations and their hyperbolic modifications, non-local hydrodynamic-type models, searching for physically significant solutions and investigating their stability and attracting properties.